/*
 * Copyright (c) 2012, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
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package java.util.stream;

import java.nio.charset.Charset;
import java.nio.file.Files;
import java.nio.file.Path;
import java.util.Arrays;
import java.util.Collection;
import java.util.Comparator;
import java.util.Iterator;
import java.util.Objects;
import java.util.Optional;
import java.util.Spliterator;
import java.util.Spliterators;
import java.util.concurrent.ConcurrentHashMap;
import java.util.function.BiConsumer;
import java.util.function.BiFunction;
import java.util.function.BinaryOperator;
import java.util.function.Consumer;
import java.util.function.Function;
import java.util.function.IntFunction;
import java.util.function.Predicate;
import java.util.function.Supplier;
import java.util.function.ToDoubleFunction;
import java.util.function.ToIntFunction;
import java.util.function.ToLongFunction;
import java.util.function.UnaryOperator;

/**
 * A sequence of elements supporting sequential and parallel aggregate
 * operations.  The following example illustrates an aggregate operation using
 * {@link Stream} and {@link IntStream}:
 *
 * <pre>{@code
 *     int sum = widgets.stream()
 *                      .filter(w -> w.getColor() == RED)
 *                      .mapToInt(w -> w.getWeight())
 *                      .sum();
 * }</pre>
 *
 * In this example, {@code widgets} is a {@code Collection<Widget>}.  We create
 * a stream of {@code Widget} objects via {@link Collection#stream Collection.stream()},
 * filter it to produce a stream containing only the red widgets, and then
 * transform it into a stream of {@code int} values representing the weight of
 * each red widget. Then this stream is summed to produce a total weight.
 *
 * <p>In addition to {@code Stream}, which is a stream of object references,
 * there are primitive specializations for {@link IntStream}, {@link LongStream},
 * and {@link DoubleStream}, all of which are referred to as "streams" and
 * conform to the characteristics and restrictions described here.
 *
 * <p>To perform a computation, stream
 * <a href="package-summary.html#StreamOps">operations</a> are composed into a
 * <em>stream pipeline</em>.  A stream pipeline consists of a source (which
 * might be an array, a collection, a generator function, an I/O channel,
 * etc), zero or more <em>intermediate operations</em> (which transform a
 * stream into another stream, such as {@link Stream#filter(Predicate)}), and a
 * <em>terminal operation</em> (which produces a result or side-effect, such
 * as {@link Stream#count()} or {@link Stream#forEach(Consumer)}).
 * Streams are lazy; computation on the source data is only performed when the
 * terminal operation is initiated, and source elements are consumed only
 * as needed.
 *
 * <p>Collections and streams, while bearing some superficial similarities,
 * have different goals.  Collections are primarily concerned with the efficient
 * management of, and access to, their elements.  By contrast, streams do not
 * provide a means to directly access or manipulate their elements, and are
 * instead concerned with declaratively describing their source and the
 * computational operations which will be performed in aggregate on that source.
 * However, if the provided stream operations do not offer the desired
 * functionality, the {@link #iterator()} and {@link #spliterator()} operations
 * can be used to perform a controlled traversal.
 *
 * <p>A stream pipeline, like the "widgets" example above, can be viewed as
 * a <em>query</em> on the stream source.  Unless the source was explicitly
 * designed for concurrent modification (such as a {@link ConcurrentHashMap}),
 * unpredictable or erroneous behavior may result from modifying the stream
 * source while it is being queried.
 *
 * <p>Most stream operations accept parameters that describe user-specified
 * behavior, such as the lambda expression {@code w -> w.getWeight()} passed to
 * {@code mapToInt} in the example above.  To preserve correct behavior,
 * these <em>behavioral parameters</em>:
 * <ul>
 * <li>must be <a href="package-summary.html#NonInterference">non-interfering</a>
 * (they do not modify the stream source); and</li>
 * <li>in most cases must be <a href="package-summary.html#Statelessness">stateless</a>
 * (their result should not depend on any state that might change during execution
 * of the stream pipeline).</li>
 * </ul>
 *
 * <p>Such parameters are always instances of a
 * <a href="../function/package-summary.html">functional interface</a> such
 * as {@link java.util.function.Function}, and are often lambda expressions or
 * method references.  Unless otherwise specified these parameters must be
 * <em>non-null</em>.
 *
 * <p>A stream should be operated on (invoking an intermediate or terminal stream
 * operation) only once.  This rules out, for example, "forked" streams, where
 * the same source feeds two or more pipelines, or multiple traversals of the
 * same stream.  A stream implementation may throw {@link IllegalStateException}
 * if it detects that the stream is being reused. However, since some stream
 * operations may return their receiver rather than a new stream object, it may
 * not be possible to detect reuse in all cases.
 *
 * <p>Streams have a {@link #close()} method and implement {@link AutoCloseable},
 * but nearly all stream instances do not actually need to be closed after use.
 * Generally, only streams whose source is an IO channel (such as those returned
 * by {@link Files#lines(Path, Charset)}) will require closing.  Most streams
 * are backed by collections, arrays, or generating functions, which require no
 * special resource management.  (If a stream does require closing, it can be
 * declared as a resource in a {@code try}-with-resources statement.)
 *
 * <p>Stream pipelines may execute either sequentially or in
 * <a href="package-summary.html#Parallelism">parallel</a>.  This
 * execution mode is a property of the stream.  Streams are created
 * with an initial choice of sequential or parallel execution.  (For example,
 * {@link Collection#stream() Collection.stream()} creates a sequential stream,
 * and {@link Collection#parallelStream() Collection.parallelStream()} creates
 * a parallel one.)  This choice of execution mode may be modified by the
 * {@link #sequential()} or {@link #parallel()} methods, and may be queried with
 * the {@link #isParallel()} method.
 *
 * @param <T> the type of the stream elements
 * @see IntStream
 * @see LongStream
 * @see DoubleStream
 * @see <a href="package-summary.html">java.util.stream</a>
 * @since 1.8
 */
public interface Stream<T> extends BaseStream<T, Stream<T>> {

  /**
   * Returns a stream consisting of the elements of this stream that match
   * the given predicate.
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> predicate to apply to each element to
   * determine if it should be included
   * @return the new stream
   */
  Stream<T> filter(Predicate<? super T> predicate);

  /**
   * Returns a stream consisting of the results of applying the given
   * function to the elements of this stream.
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param <R> The element type of the new stream
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element
   * @return the new stream
   */
  <R> Stream<R> map(Function<? super T, ? extends R> mapper);

  /**
   * Returns an {@code IntStream} consisting of the results of applying the
   * given function to the elements of this stream.
   *
   * <p>This is an <a href="package-summary.html#StreamOps">
   * intermediate operation</a>.
   *
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element
   * @return the new stream
   */
  IntStream mapToInt(ToIntFunction<? super T> mapper);

  /**
   * Returns a {@code LongStream} consisting of the results of applying the
   * given function to the elements of this stream.
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element
   * @return the new stream
   */
  LongStream mapToLong(ToLongFunction<? super T> mapper);

  /**
   * Returns a {@code DoubleStream} consisting of the results of applying the
   * given function to the elements of this stream.
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element
   * @return the new stream
   */
  DoubleStream mapToDouble(ToDoubleFunction<? super T> mapper);

  /**
   * Returns a stream consisting of the results of replacing each element of
   * this stream with the contents of a mapped stream produced by applying
   * the provided mapping function to each element.  Each mapped stream is
   * {@link java.util.stream.BaseStream#close() closed} after its contents
   * have been placed into this stream.  (If a mapped stream is {@code null}
   * an empty stream is used, instead.)
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param <R> The element type of the new stream
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element which
   * produces a stream of new values
   * @return the new stream
   * @apiNote The {@code flatMap()} operation has the effect of applying a one-to-many
   * transformation to the elements of the stream, and then flattening the resulting elements into a
   * new stream.
   *
   * <p><b>Examples.</b>
   *
   * <p>If {@code orders} is a stream of purchase orders, and each purchase order contains a
   * collection of line items, then the following produces a stream containing all the line items in
   * all the orders:
   * <pre>{@code
   *     orders.flatMap(order -> order.getLineItems().stream())...
   * }</pre>
   *
   * <p>If {@code path} is the path to a file, then the following produces a stream of the {@code
   * words} contained in that file:
   * <pre>{@code
   *     Stream<String> lines = Files.lines(path, StandardCharsets.UTF_8);
   *     Stream<String> words = lines.flatMap(line -> Stream.of(line.split(" +")));
   * }</pre>
   * The {@code mapper} function passed to {@code flatMap} splits a line, using a simple regular
   * expression, into an array of words, and then creates a stream of words from that array.
   */
  <R> Stream<R> flatMap(Function<? super T, ? extends Stream<? extends R>> mapper);

  /**
   * Returns an {@code IntStream} consisting of the results of replacing each
   * element of this stream with the contents of a mapped stream produced by
   * applying the provided mapping function to each element.  Each mapped
   * stream is {@link java.util.stream.BaseStream#close() closed} after its
   * contents have been placed into this stream.  (If a mapped stream is
   * {@code null} an empty stream is used, instead.)
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element which
   * produces a stream of new values
   * @return the new stream
   * @see #flatMap(Function)
   */
  IntStream flatMapToInt(Function<? super T, ? extends IntStream> mapper);

  /**
   * Returns an {@code LongStream} consisting of the results of replacing each
   * element of this stream with the contents of a mapped stream produced by
   * applying the provided mapping function to each element.  Each mapped
   * stream is {@link java.util.stream.BaseStream#close() closed} after its
   * contents have been placed into this stream.  (If a mapped stream is
   * {@code null} an empty stream is used, instead.)
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element which
   * produces a stream of new values
   * @return the new stream
   * @see #flatMap(Function)
   */
  LongStream flatMapToLong(Function<? super T, ? extends LongStream> mapper);

  /**
   * Returns an {@code DoubleStream} consisting of the results of replacing
   * each element of this stream with the contents of a mapped stream produced
   * by applying the provided mapping function to each element.  Each mapped
   * stream is {@link java.util.stream.BaseStream#close() closed} after its
   * contents have placed been into this stream.  (If a mapped stream is
   * {@code null} an empty stream is used, instead.)
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * @param mapper a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function to apply to each element which
   * produces a stream of new values
   * @return the new stream
   * @see #flatMap(Function)
   */
  DoubleStream flatMapToDouble(Function<? super T, ? extends DoubleStream> mapper);

  /**
   * Returns a stream consisting of the distinct elements (according to
   * {@link Object#equals(Object)}) of this stream.
   *
   * <p>For ordered streams, the selection of distinct elements is stable
   * (for duplicated elements, the element appearing first in the encounter
   * order is preserved.)  For unordered streams, no stability guarantees
   * are made.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">stateful
   * intermediate operation</a>.
   *
   * @return the new stream
   * @apiNote Preserving stability for {@code distinct()} in parallel pipelines is relatively
   * expensive (requires that the operation act as a full barrier, with substantial buffering
   * overhead), and stability is often not needed. Using an unordered stream source (such as {@link
   * #generate(Supplier)}) or removing the ordering constraint with {@link #unordered()} may result
   * in significantly more efficient execution for {@code distinct()} in parallel pipelines, if the
   * semantics of your situation permit.  If consistency with encounter order is required, and you
   * are experiencing poor performance or memory utilization with {@code distinct()} in parallel
   * pipelines, switching to sequential execution with {@link #sequential()} may improve
   * performance.
   */
  Stream<T> distinct();

  /**
   * Returns a stream consisting of the elements of this stream, sorted
   * according to natural order.  If the elements of this stream are not
   * {@code Comparable}, a {@code java.lang.ClassCastException} may be thrown
   * when the terminal operation is executed.
   *
   * <p>For ordered streams, the sort is stable.  For unordered streams, no
   * stability guarantees are made.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">stateful
   * intermediate operation</a>.
   *
   * @return the new stream
   */
  Stream<T> sorted();

  /**
   * Returns a stream consisting of the elements of this stream, sorted
   * according to the provided {@code Comparator}.
   *
   * <p>For ordered streams, the sort is stable.  For unordered streams, no
   * stability guarantees are made.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">stateful
   * intermediate operation</a>.
   *
   * @param comparator a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> {@code Comparator} to be used to
   * compare stream elements
   * @return the new stream
   */
  Stream<T> sorted(Comparator<? super T> comparator);

  /**
   * Returns a stream consisting of the elements of this stream, additionally
   * performing the provided action on each element as elements are consumed
   * from the resulting stream.
   *
   * <p>This is an <a href="package-summary.html#StreamOps">intermediate
   * operation</a>.
   *
   * <p>For parallel stream pipelines, the action may be called at
   * whatever time and in whatever thread the element is made available by the
   * upstream operation.  If the action modifies shared state,
   * it is responsible for providing the required synchronization.
   *
   * @param action a <a href="package-summary.html#NonInterference"> non-interfering</a> action to
   * perform on the elements as they are consumed from the stream
   * @return the new stream
   * @apiNote This method exists mainly to support debugging, where you want to see the elements as
   * they flow past a certain point in a pipeline:
   * <pre>{@code
   *     Stream.of("one", "two", "three", "four")
   *         .filter(e -> e.length() > 3)
   *         .peek(e -> System.out.println("Filtered value: " + e))
   *         .map(String::toUpperCase)
   *         .peek(e -> System.out.println("Mapped value: " + e))
   *         .collect(Collectors.toList());
   * }</pre>
   */
  Stream<T> peek(Consumer<? super T> action);

  /**
   * Returns a stream consisting of the elements of this stream, truncated
   * to be no longer than {@code maxSize} in length.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
   * stateful intermediate operation</a>.
   *
   * @param maxSize the number of elements the stream should be limited to
   * @return the new stream
   * @throws IllegalArgumentException if {@code maxSize} is negative
   * @apiNote While {@code limit()} is generally a cheap operation on sequential stream pipelines,
   * it can be quite expensive on ordered parallel pipelines, especially for large values of {@code
   * maxSize}, since {@code limit(n)} is constrained to return not just any <em>n</em> elements, but
   * the <em>first n</em> elements in the encounter order.  Using an unordered stream source (such
   * as {@link #generate(Supplier)}) or removing the ordering constraint with {@link #unordered()}
   * may result in significant speedups of {@code limit()} in parallel pipelines, if the semantics
   * of your situation permit.  If consistency with encounter order is required, and you are
   * experiencing poor performance or memory utilization with {@code limit()} in parallel pipelines,
   * switching to sequential execution with {@link #sequential()} may improve performance.
   */
  Stream<T> limit(long maxSize);

  /**
   * Returns a stream consisting of the remaining elements of this stream
   * after discarding the first {@code n} elements of the stream.
   * If this stream contains fewer than {@code n} elements then an
   * empty stream will be returned.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">stateful
   * intermediate operation</a>.
   *
   * @param n the number of leading elements to skip
   * @return the new stream
   * @throws IllegalArgumentException if {@code n} is negative
   * @apiNote While {@code skip()} is generally a cheap operation on sequential stream pipelines, it
   * can be quite expensive on ordered parallel pipelines, especially for large values of {@code n},
   * since {@code skip(n)} is constrained to skip not just any <em>n</em> elements, but the
   * <em>first n</em> elements in the encounter order.  Using an unordered stream source (such as
   * {@link #generate(Supplier)}) or removing the ordering constraint with {@link #unordered()} may
   * result in significant speedups of {@code skip()} in parallel pipelines, if the semantics of
   * your situation permit.  If consistency with encounter order is required, and you are
   * experiencing poor performance or memory utilization with {@code skip()} in parallel pipelines,
   * switching to sequential execution with {@link #sequential()} may improve performance.
   */
  Stream<T> skip(long n);

  /**
   * Performs an action for each element of this stream.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * <p>The behavior of this operation is explicitly nondeterministic.
   * For parallel stream pipelines, this operation does <em>not</em>
   * guarantee to respect the encounter order of the stream, as doing so
   * would sacrifice the benefit of parallelism.  For any given element, the
   * action may be performed at whatever time and in whatever thread the
   * library chooses.  If the action accesses shared state, it is
   * responsible for providing the required synchronization.
   *
   * @param action a <a href="package-summary.html#NonInterference"> non-interfering</a> action to
   * perform on the elements
   */
  void forEach(Consumer<? super T> action);

  /**
   * Performs an action for each element of this stream, in the encounter
   * order of the stream if the stream has a defined encounter order.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * <p>This operation processes the elements one at a time, in encounter
   * order if one exists.  Performing the action for one element
   * <a href="../concurrent/package-summary.html#MemoryVisibility"><i>happens-before</i></a>
   * performing the action for subsequent elements, but for any given element,
   * the action may be performed in whatever thread the library chooses.
   *
   * @param action a <a href="package-summary.html#NonInterference"> non-interfering</a> action to
   * perform on the elements
   * @see #forEach(Consumer)
   */
  void forEachOrdered(Consumer<? super T> action);

  /**
   * Returns an array containing the elements of this stream.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @return an array containing the elements of this stream
   */
  Object[] toArray();

  /**
   * Returns an array containing the elements of this stream, using the
   * provided {@code generator} function to allocate the returned array, as
   * well as any additional arrays that might be required for a partitioned
   * execution or for resizing.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @param <A> the element type of the resulting array
   * @param generator a function which produces a new array of the desired type and the provided
   * length
   * @return an array containing the elements in this stream
   * @throws ArrayStoreException if the runtime type of the array returned from the array generator
   * is not a supertype of the runtime type of every element in this stream
   * @apiNote The generator function takes an integer, which is the size of the desired array, and
   * produces an array of the desired size.  This can be concisely expressed with an array
   * constructor reference:
   * <pre>{@code
   *     Person[] men = people.stream()
   *                          .filter(p -> p.getGender() == MALE)
   *                          .toArray(Person[]::new);
   * }</pre>
   */
  <A> A[] toArray(IntFunction<A[]> generator);

  /**
   * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
   * elements of this stream, using the provided identity value and an
   * <a href="package-summary.html#Associativity">associative</a>
   * accumulation function, and returns the reduced value.  This is equivalent
   * to:
   * <pre>{@code
   *     T result = identity;
   *     for (T element : this stream)
   *         result = accumulator.apply(result, element)
   *     return result;
   * }</pre>
   *
   * but is not constrained to execute sequentially.
   *
   * <p>The {@code identity} value must be an identity for the accumulator
   * function. This means that for all {@code t},
   * {@code accumulator.apply(identity, t)} is equal to {@code t}.
   * The {@code accumulator} function must be an
   * <a href="package-summary.html#Associativity">associative</a> function.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @param identity the identity value for the accumulating function
   * @param accumulator an <a href="package-summary.html#Associativity">associative</a>, <a
   * href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function for combining two values
   * @return the result of the reduction
   * @apiNote Sum, min, max, average, and string concatenation are all special cases of reduction.
   * Summing a stream of numbers can be expressed as:
   *
   * <pre>{@code
   *     Integer sum = integers.reduce(0, (a, b) -> a+b);
   * }</pre>
   *
   * or:
   *
   * <pre>{@code
   *     Integer sum = integers.reduce(0, Integer::sum);
   * }</pre>
   *
   * <p>While this may seem a more roundabout way to perform an aggregation compared to simply
   * mutating a running total in a loop, reduction operations parallelize more gracefully, without
   * needing additional synchronization and with greatly reduced risk of data races.
   */
  T reduce(T identity, BinaryOperator<T> accumulator);

  /**
   * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
   * elements of this stream, using an
   * <a href="package-summary.html#Associativity">associative</a> accumulation
   * function, and returns an {@code Optional} describing the reduced value,
   * if any. This is equivalent to:
   * <pre>{@code
   *     boolean foundAny = false;
   *     T result = null;
   *     for (T element : this stream) {
   *         if (!foundAny) {
   *             foundAny = true;
   *             result = element;
   *         }
   *         else
   *             result = accumulator.apply(result, element);
   *     }
   *     return foundAny ? Optional.of(result) : Optional.empty();
   * }</pre>
   *
   * but is not constrained to execute sequentially.
   *
   * <p>The {@code accumulator} function must be an
   * <a href="package-summary.html#Associativity">associative</a> function.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @param accumulator an <a href="package-summary.html#Associativity">associative</a>, <a
   * href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function for combining two values
   * @return an {@link Optional} describing the result of the reduction
   * @throws NullPointerException if the result of the reduction is null
   * @see #reduce(Object, BinaryOperator)
   * @see #min(Comparator)
   * @see #max(Comparator)
   */
  Optional<T> reduce(BinaryOperator<T> accumulator);

  /**
   * Performs a <a href="package-summary.html#Reduction">reduction</a> on the
   * elements of this stream, using the provided identity, accumulation and
   * combining functions.  This is equivalent to:
   * <pre>{@code
   *     U result = identity;
   *     for (T element : this stream)
   *         result = accumulator.apply(result, element)
   *     return result;
   * }</pre>
   *
   * but is not constrained to execute sequentially.
   *
   * <p>The {@code identity} value must be an identity for the combiner
   * function.  This means that for all {@code u}, {@code combiner(identity, u)}
   * is equal to {@code u}.  Additionally, the {@code combiner} function
   * must be compatible with the {@code accumulator} function; for all
   * {@code u} and {@code t}, the following must hold:
   * <pre>{@code
   *     combiner.apply(u, accumulator.apply(identity, t)) == accumulator.apply(u, t)
   * }</pre>
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @param <U> The type of the result
   * @param identity the identity value for the combiner function
   * @param accumulator an <a href="package-summary.html#Associativity">associative</a>, <a
   * href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function for incorporating an
   * additional element into a result
   * @param combiner an <a href="package-summary.html#Associativity">associative</a>, <a
   * href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function for combining two values,
   * which must be compatible with the accumulator function
   * @return the result of the reduction
   * @apiNote Many reductions using this form can be represented more simply by an explicit
   * combination of {@code map} and {@code reduce} operations. The {@code accumulator} function acts
   * as a fused mapper and accumulator, which can sometimes be more efficient than separate mapping
   * and reduction, such as when knowing the previously reduced value allows you to avoid some
   * computation.
   * @see #reduce(BinaryOperator)
   * @see #reduce(Object, BinaryOperator)
   */
  <U> U reduce(U identity,
      BiFunction<U, ? super T, U> accumulator,
      BinaryOperator<U> combiner);

  /**
   * Performs a <a href="package-summary.html#MutableReduction">mutable
   * reduction</a> operation on the elements of this stream.  A mutable
   * reduction is one in which the reduced value is a mutable result container,
   * such as an {@code ArrayList}, and elements are incorporated by updating
   * the state of the result rather than by replacing the result.  This
   * produces a result equivalent to:
   * <pre>{@code
   *     R result = supplier.get();
   *     for (T element : this stream)
   *         accumulator.accept(result, element);
   *     return result;
   * }</pre>
   *
   * <p>Like {@link #reduce(Object, BinaryOperator)}, {@code collect} operations
   * can be parallelized without requiring additional synchronization.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @param <R> type of the result
   * @param supplier a function that creates a new result container. For a parallel execution, this
   * function may be called multiple times and must return a fresh value each time.
   * @param accumulator an <a href="package-summary.html#Associativity">associative</a>, <a
   * href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function for incorporating an
   * additional element into a result
   * @param combiner an <a href="package-summary.html#Associativity">associative</a>, <a
   * href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> function for combining two values,
   * which must be compatible with the accumulator function
   * @return the result of the reduction
   * @apiNote There are many existing classes in the JDK whose signatures are well-suited for use
   * with method references as arguments to {@code collect()}. For example, the following will
   * accumulate strings into an {@code ArrayList}:
   * <pre>{@code
   *     List<String> asList = stringStream.collect(ArrayList::new, ArrayList::add,
   *                                                ArrayList::addAll);
   * }</pre>
   *
   * <p>The following will take a stream of strings and concatenates them into a single string:
   * <pre>{@code
   *     String concat = stringStream.collect(StringBuilder::new, StringBuilder::append,
   *                                          StringBuilder::append)
   *                                 .toString();
   * }</pre>
   */
  <R> R collect(Supplier<R> supplier,
      BiConsumer<R, ? super T> accumulator,
      BiConsumer<R, R> combiner);

  /**
   * Performs a <a href="package-summary.html#MutableReduction">mutable
   * reduction</a> operation on the elements of this stream using a
   * {@code Collector}.  A {@code Collector}
   * encapsulates the functions used as arguments to
   * {@link #collect(Supplier, BiConsumer, BiConsumer)}, allowing for reuse of
   * collection strategies and composition of collect operations such as
   * multiple-level grouping or partitioning.
   *
   * <p>If the stream is parallel, and the {@code Collector}
   * is {@link Collector.Characteristics#CONCURRENT concurrent}, and
   * either the stream is unordered or the collector is
   * {@link Collector.Characteristics#UNORDERED unordered},
   * then a concurrent reduction will be performed (see {@link Collector} for
   * details on concurrent reduction.)
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * <p>When executed in parallel, multiple intermediate results may be
   * instantiated, populated, and merged so as to maintain isolation of
   * mutable data structures.  Therefore, even when executed in parallel
   * with non-thread-safe data structures (such as {@code ArrayList}), no
   * additional synchronization is needed for a parallel reduction.
   *
   * @param <R> the type of the result
   * @param <A> the intermediate accumulation type of the {@code Collector}
   * @param collector the {@code Collector} describing the reduction
   * @return the result of the reduction
   * @apiNote The following will accumulate strings into an ArrayList:
   * <pre>{@code
   *     List<String> asList = stringStream.collect(Collectors.toList());
   * }</pre>
   *
   * <p>The following will classify {@code Person} objects by city:
   * <pre>{@code
   *     Map<String, List<Person>> peopleByCity
   *         = personStream.collect(Collectors.groupingBy(Person::getCity));
   * }</pre>
   *
   * <p>The following will classify {@code Person} objects by state and city, cascading two {@code
   * Collector}s together:
   * <pre>{@code
   *     Map<String, Map<String, List<Person>>> peopleByStateAndCity
   *         = personStream.collect(Collectors.groupingBy(Person::getState,
   *                                                      Collectors.groupingBy(Person::getCity)));
   * }</pre>
   * @see #collect(Supplier, BiConsumer, BiConsumer)
   * @see Collectors
   */
  <R, A> R collect(Collector<? super T, A, R> collector);

  /**
   * Returns the minimum element of this stream according to the provided
   * {@code Comparator}.  This is a special case of a
   * <a href="package-summary.html#Reduction">reduction</a>.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal operation</a>.
   *
   * @param comparator a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> {@code Comparator} to compare elements
   * of this stream
   * @return an {@code Optional} describing the minimum element of this stream, or an empty {@code
   * Optional} if the stream is empty
   * @throws NullPointerException if the minimum element is null
   */
  Optional<T> min(Comparator<? super T> comparator);

  /**
   * Returns the maximum element of this stream according to the provided
   * {@code Comparator}.  This is a special case of a
   * <a href="package-summary.html#Reduction">reduction</a>.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal
   * operation</a>.
   *
   * @param comparator a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> {@code Comparator} to compare elements
   * of this stream
   * @return an {@code Optional} describing the maximum element of this stream, or an empty {@code
   * Optional} if the stream is empty
   * @throws NullPointerException if the maximum element is null
   */
  Optional<T> max(Comparator<? super T> comparator);

  /**
   * Returns the count of elements in this stream.  This is a special case of
   * a <a href="package-summary.html#Reduction">reduction</a> and is
   * equivalent to:
   * <pre>{@code
   *     return mapToLong(e -> 1L).sum();
   * }</pre>
   *
   * <p>This is a <a href="package-summary.html#StreamOps">terminal operation</a>.
   *
   * @return the count of elements in this stream
   */
  long count();

  /**
   * Returns whether any elements of this stream match the provided
   * predicate.  May not evaluate the predicate on all elements if not
   * necessary for determining the result.  If the stream is empty then
   * {@code false} is returned and the predicate is not evaluated.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
   * terminal operation</a>.
   *
   * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> predicate to apply to elements of this
   * stream
   * @return {@code true} if any elements of the stream match the provided predicate, otherwise
   * {@code false}
   * @apiNote This method evaluates the <em>existential quantification</em> of the predicate over
   * the elements of the stream (for some x P(x)).
   */
  boolean anyMatch(Predicate<? super T> predicate);

  /**
   * Returns whether all elements of this stream match the provided predicate.
   * May not evaluate the predicate on all elements if not necessary for
   * determining the result.  If the stream is empty then {@code true} is
   * returned and the predicate is not evaluated.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
   * terminal operation</a>.
   *
   * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> predicate to apply to elements of this
   * stream
   * @return {@code true} if either all elements of the stream match the provided predicate or the
   * stream is empty, otherwise {@code false}
   * @apiNote This method evaluates the <em>universal quantification</em> of the predicate over the
   * elements of the stream (for all x P(x)).  If the stream is empty, the quantification is said to
   * be <em>vacuously satisfied</em> and is always {@code true} (regardless of P(x)).
   */
  boolean allMatch(Predicate<? super T> predicate);

  /**
   * Returns whether no elements of this stream match the provided predicate.
   * May not evaluate the predicate on all elements if not necessary for
   * determining the result.  If the stream is empty then {@code true} is
   * returned and the predicate is not evaluated.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
   * terminal operation</a>.
   *
   * @param predicate a <a href="package-summary.html#NonInterference">non-interfering</a>, <a
   * href="package-summary.html#Statelessness">stateless</a> predicate to apply to elements of this
   * stream
   * @return {@code true} if either no elements of the stream match the provided predicate or the
   * stream is empty, otherwise {@code false}
   * @apiNote This method evaluates the <em>universal quantification</em> of the negated predicate
   * over the elements of the stream (for all x ~P(x)).  If the stream is empty, the quantification
   * is said to be vacuously satisfied and is always {@code true}, regardless of P(x).
   */
  boolean noneMatch(Predicate<? super T> predicate);

  /**
   * Returns an {@link Optional} describing the first element of this stream,
   * or an empty {@code Optional} if the stream is empty.  If the stream has
   * no encounter order, then any element may be returned.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
   * terminal operation</a>.
   *
   * @return an {@code Optional} describing the first element of this stream, or an empty {@code
   * Optional} if the stream is empty
   * @throws NullPointerException if the element selected is null
   */
  Optional<T> findFirst();

  /**
   * Returns an {@link Optional} describing some element of the stream, or an
   * empty {@code Optional} if the stream is empty.
   *
   * <p>This is a <a href="package-summary.html#StreamOps">short-circuiting
   * terminal operation</a>.
   *
   * <p>The behavior of this operation is explicitly nondeterministic; it is
   * free to select any element in the stream.  This is to allow for maximal
   * performance in parallel operations; the cost is that multiple invocations
   * on the same source may not return the same result.  (If a stable result
   * is desired, use {@link #findFirst()} instead.)
   *
   * @return an {@code Optional} describing some element of this stream, or an empty {@code
   * Optional} if the stream is empty
   * @throws NullPointerException if the element selected is null
   * @see #findFirst()
   */
  Optional<T> findAny();

  // Static factories

  /**
   * Returns a builder for a {@code Stream}.
   *
   * @param <T> type of elements
   * @return a stream builder
   */
  public static <T> Builder<T> builder() {
    return new Streams.StreamBuilderImpl<>();
  }

  /**
   * Returns an empty sequential {@code Stream}.
   *
   * @param <T> the type of stream elements
   * @return an empty sequential stream
   */
  public static <T> Stream<T> empty() {
    return StreamSupport.stream(Spliterators.<T>emptySpliterator(), false);
  }

  /**
   * Returns a sequential {@code Stream} containing a single element.
   *
   * @param t the single element
   * @param <T> the type of stream elements
   * @return a singleton sequential stream
   */
  public static <T> Stream<T> of(T t) {
    return StreamSupport.stream(new Streams.StreamBuilderImpl<>(t), false);
  }

  /**
   * Returns a sequential ordered stream whose elements are the specified values.
   *
   * @param <T> the type of stream elements
   * @param values the elements of the new stream
   * @return the new stream
   */
  @SafeVarargs
  @SuppressWarnings("varargs") // Creating a stream from an array is safe
  public static <T> Stream<T> of(T... values) {
    return Arrays.stream(values);
  }

  /**
   * Returns an infinite sequential ordered {@code Stream} produced by iterative
   * application of a function {@code f} to an initial element {@code seed},
   * producing a {@code Stream} consisting of {@code seed}, {@code f(seed)},
   * {@code f(f(seed))}, etc.
   *
   * <p>The first element (position {@code 0}) in the {@code Stream} will be
   * the provided {@code seed}.  For {@code n > 0}, the element at position
   * {@code n}, will be the result of applying the function {@code f} to the
   * element at position {@code n - 1}.
   *
   * @param <T> the type of stream elements
   * @param seed the initial element
   * @param f a function to be applied to to the previous element to produce a new element
   * @return a new sequential {@code Stream}
   */
  public static <T> Stream<T> iterate(final T seed, final UnaryOperator<T> f) {
    Objects.requireNonNull(f);
    final Iterator<T> iterator = new Iterator<T>() {
      @SuppressWarnings("unchecked")
      T t = (T) Streams.NONE;

      @Override
      public boolean hasNext() {
        return true;
      }

      @Override
      public T next() {
        return t = (t == Streams.NONE) ? seed : f.apply(t);
      }
    };
    return StreamSupport.stream(Spliterators.spliteratorUnknownSize(
        iterator,
        Spliterator.ORDERED | Spliterator.IMMUTABLE), false);
  }

  /**
   * Returns an infinite sequential unordered stream where each element is
   * generated by the provided {@code Supplier}.  This is suitable for
   * generating constant streams, streams of random elements, etc.
   *
   * @param <T> the type of stream elements
   * @param s the {@code Supplier} of generated elements
   * @return a new infinite sequential unordered {@code Stream}
   */
  public static <T> Stream<T> generate(Supplier<T> s) {
    Objects.requireNonNull(s);
    return StreamSupport.stream(
        new StreamSpliterators.InfiniteSupplyingSpliterator.OfRef<>(Long.MAX_VALUE, s), false);
  }

  /**
   * Creates a lazily concatenated stream whose elements are all the
   * elements of the first stream followed by all the elements of the
   * second stream.  The resulting stream is ordered if both
   * of the input streams are ordered, and parallel if either of the input
   * streams is parallel.  When the resulting stream is closed, the close
   * handlers for both input streams are invoked.
   *
   * @param <T> The type of stream elements
   * @param a the first stream
   * @param b the second stream
   * @return the concatenation of the two input streams
   * @implNote Use caution when constructing streams from repeated concatenation. Accessing an
   * element of a deeply concatenated stream can result in deep call chains, or even {@code
   * StackOverflowException}.
   */
  public static <T> Stream<T> concat(Stream<? extends T> a, Stream<? extends T> b) {
    Objects.requireNonNull(a);
    Objects.requireNonNull(b);

    @SuppressWarnings("unchecked")
    Spliterator<T> split = new Streams.ConcatSpliterator.OfRef<>(
        (Spliterator<T>) a.spliterator(), (Spliterator<T>) b.spliterator());
    Stream<T> stream = StreamSupport.stream(split, a.isParallel() || b.isParallel());
    return stream.onClose(Streams.composedClose(a, b));
  }

  /**
   * A mutable builder for a {@code Stream}.  This allows the creation of a
   * {@code Stream} by generating elements individually and adding them to the
   * {@code Builder} (without the copying overhead that comes from using
   * an {@code ArrayList} as a temporary buffer.)
   *
   * <p>A stream builder has a lifecycle, which starts in a building
   * phase, during which elements can be added, and then transitions to a built
   * phase, after which elements may not be added.  The built phase begins
   * when the {@link #build()} method is called, which creates an ordered
   * {@code Stream} whose elements are the elements that were added to the stream
   * builder, in the order they were added.
   *
   * @param <T> the type of stream elements
   * @see Stream#builder()
   * @since 1.8
   */
  public interface Builder<T> extends Consumer<T> {

    /**
     * Adds an element to the stream being built.
     *
     * @throws IllegalStateException if the builder has already transitioned to the built state
     */
    @Override
    void accept(T t);

    /**
     * Adds an element to the stream being built.
     *
     * @param t the element to add
     * @return {@code this} builder
     * @throws IllegalStateException if the builder has already transitioned to the built state
     * @implSpec The default implementation behaves as if:
     * <pre>{@code
     *     accept(t)
     *     return this;
     * }</pre>
     */
    default Builder<T> add(T t) {
      accept(t);
      return this;
    }

    /**
     * Builds the stream, transitioning this builder to the built state.
     * An {@code IllegalStateException} is thrown if there are further attempts
     * to operate on the builder after it has entered the built state.
     *
     * @return the built stream
     * @throws IllegalStateException if the builder has already transitioned to the built state
     */
    Stream<T> build();

  }
}
